A Compact Super Resolution Phase Retrieval Method for Fourier Measurement

The method of super-resolution phase retrieval (PR) for Fourier phaseless measurement extends the signal model of PR from the discrete domain to a more realistic continuous domain. However, the existing three-stage solving framework contains unnecessary redundancy, so its core steps are loosely connected and have high computational complexity. Aiming at this, new algorithms are proposed for the following two key steps respectively, so as to achieve a compact super-resolution PR framework. First, for the super-resolution stage of the auto-correlation function (ACF), a non-redundant algorithm is proposed by merging items containing the same information. Then, a low complexity iterative algorithm is proposed for the support recovery by employing the relationship of elements we obtain from the previous step. Sufficient numerical simulations verify the effectiveness of the proposed algorithms and each step has better noise robustness compared with the existing method, but worse robustness when they combine. Therefore, we test the performance of different subalgorithm combination strategies, providing insight in meeting diverse requirements for noise robustness and computational complexity. Moreover, the effectiveness of the proposed method in a real system is verified by hardware experiment.